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An airplane is heading north at an airspeed of 700 km/hr, but there is a wind blowing from the northeast at 40 km/hr.

The plane will end up flying  ______ degrees off course.

The plane's speed relative to the ground will be  _____ km/hr.

Sofiya.K  Mar 2, 2018
 #1
avatar+13665 
+1

Break the two speeds into their x and y components...then add them together

 

Airplane  ax=0  ay=700

Wind      wx= -40 cos45    wy= -40sin45     (see diagram)

                     = -28.28             = -28.28

 

Add together for the RESULTANT

x=-28.28   y = 700-28.28= 671.71

 

Degrees off course will be arctan (-28.28/671.71) = 2.41 degrees off course to the west

 

Speed will be   sqrt ( x^2 + y^2) = 672.3 km/hr

ElectricPavlov  Mar 2, 2018
 #2
avatar+13665 
+1

Here is the diagram of the info given:

 

ElectricPavlov  Mar 2, 2018

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